%%%
% Balance
%%%
\def\filedateBalance{2025/05/28}%
\def\fileversionBalance{0.1c}%
\message{-- \filedateBalance\space v\fileversionBalance}%
%
\newtoks\tokPlateauGauche%
\newtoks\tokPlateauDroit%
\def\UpdatetoksPlateauGauche#1\nil{\addtotok\tokPlateauGauche{#1,}}%
\def\UpdatetoksPlateauDroit#1\nil{\addtotok\tokPlateauDroit{#1,}}%
%
\setKVdefault[Balance]{Inf=false,Sup=false,Masse=false,Codes=false,Traces={},Ecarth=0,Echelle=false,Unite=1cm,Vraisemblance={}}%
%
\NewDocumentCommand\Balance{omm}{%
  \tokPlateauGauche{}%
  \tokPlateauDroit{}%
  \useKVdefault[Balance]%
  \setKV[Balance]{#1}%
  \setsepchar{,}\ignoreemptyitems%
  \readlist*\ListePlateauGauche{#2}%
  \readlist*\ListePlateauDroit{#3}%
  \reademptyitems%
  \foreachitem\compteur\in\ListePlateauGauche{%
    \expandafter\UpdatetoksPlateauGauche\compteur\nil
  }%
  \foreachitem\compteur\in\ListePlateauDroit{%
    \expandafter\UpdatetoksPlateauDroit\compteur\nil
  }%
  \BuildBalance{\the\tokPlateauGauche}{\the\tokPlateauDroit}%
}%

\NewDocumentCommand\BuildBalance{mm}{%
    \mplibforcehmode
    \begin{mplibcode}
      u:=\useKV[Balance]{Unite};
      ecarth=\useKV[Balance]{Ecarth};
      \ifemptyKV[Balance]{Traces}{}{\useKV[Balance]{Traces};}
      %
      vardef Poids=
      save poids;
      picture poids;
      poids=image(
      path poidsext;
      poidsext=(0,0)--u*(0.4,0){dir90}..{dir180}(u*(0.2,0.4))..{dir-90}cycle;
      fill poidsext withcolor NavyBlue;
      trace cercles(u*(0.2,0.425),0.1u) withcolor NavyBlue;
      );
      poids
      enddef;

      vardef PoidsM(expr nb)=
      save poids;
      picture poids;
      poids=image(
      path poidsext;
      \ifemptyKV[Balance]{Vraisemblance}{simili:=1+0.5*(nb div 5);}{simili:=\useKV[Balance]{Vraisemblance};}
      poidsext=((0,0)--u*(0.4,0){dir90}..{dir180}(u*(0.2,0.4))..{dir-90}cycle) xscaled simili yscaled simili;
      fill poidsext withcolor NavyBlue;
      trace cercles(simili*u*(0.2,0.425),0.1u) withcolor NavyBlue;
      drawoptions(withcolor white);
      label.top(TEX("\noexpand\tiny\Masse{"&decimal(nb)&"}"),iso((0,0),u*(simili*0.4,0)));
      drawoptions();
      );
      poids
      enddef;

      boolean Sup,Inf,Masse;
      Sup=\useKV[Balance]{Sup};
      Inf=\useKV[Balance]{Inf};
      Masse=\useKV[Balance]{Masse};
      pair O,A,B,M[],N[];
      O=(0,0);
      A=u*(-0.5,0);
      B=u*(0.5,0);

      path pathgauche,pathdroite,plateau;

      if Inf:
        M1=A+u*(0,0.25);
        N1=B+u*(0,0.75);
      elseif Sup:
        M1=A+u*(0,0.75);
        N1=B+u*(0,0.25);
      else:
        M1=A+u*(0,0.5);
        N1=B+u*(0,0.5);
      fi;

      longgauche=0;
      longdroit=0;
      nbimggauche=0;
      nbimgdroit=0;
      picture Imgg[],Imgd[];
      
      for p_=#1:
        if numeric p_:
          if Masse:
            \ifemptyKV[Balance]{Vraisemblance}{simili:=1+0.5*(p_ div 5);}{simili:=\useKV[Balance]{Vraisemblance};}
            longgauche:=longgauche+u*((simili)*0.4+0.2);
          else:
            longgauche:=longgauche+p_*0.6u;
          fi;
        elseif string p_:
          nbimggauche:=nbimggauche+1;
          Imgg[nbimggauche]=image(%
          label(TEX(p_),(0,0));
          );
          longgauche:=longgauche+abs(lrcorner Imgg[nbimggauche]-llcorner Imgg[nbimggauche])+0.2u;
        else:
          longgauche:=longgauche+abs(lrcorner p_-llcorner p_)+0.2u;
        fi;
      endfor;
      for p_=#2:
        if numeric p_:
          if Masse:
            \ifemptyKV[Balance]{Vraisemblance}{simili:=1+0.5*(p_ div 5);}{simili:=\useKV[Balance]{Vraisemblance};}
            longdroit:=longdroit+u*((simili)*0.4+0.2);
          else:
            longdroit:=longdroit+p_*0.6u;
          fi;
        elseif string p_:
          nbimgdroit:=nbimgdroit+1;
          Imgd[nbimgdroit]=image(%
          label(TEX(p_),(0,0));
          );
          longdroit:=longdroit+abs(lrcorner Imgd[nbimgdroit]-llcorner Imgd[nbimgdroit])+0.2u;
        else:
          longdroit:=longdroit+abs(lrcorner p_-llcorner p_)+0.2u;
        fi;
      endfor;
      pair decalageg,decalaged;
      if longgauche>longdroit:
        M2=M1+(-longgauche,0);
        N2=N1+(longgauche,0);
        decalageg=u*(0.1,0);
        decalaged=u*(0.1,0)+(0.5*abs(longdroit-longgauche),0);
      else:
        M2=M1+(-longdroit,0);
        N2=N1+(longdroit,0);
        decalaged=u*(0.1,0);
        decalageg=u*(0.1,0)+(0.5*abs(longdroit-longgauche),0);%
      fi;
      M0=iso(M1,M2)+u*(0,-0.5);
      M3=iso(M1,M2);
      N0=symetrie(M0,O);
      N3=iso(N1,N2);
      trace N2--N1--N3--N0--O--M0--M3--M1--M2 withpen pencircle scaled 1.1;
      fill cercles(O,1.5mm);
      % Affichage des "masses"
      nbimggauche:=0;
      for p_=#1:
        if numeric p_:
          if Masse:
            trace PoidsM(p_) shifted(M1-lrcorner PoidsM(p_)-decalageg);
            \ifemptyKV[Balance]{Vraisemblance}{simili:=1+0.5*(p_ div 5);}{simili:=\useKV[Balance]{Vraisemblance};}
            decalageg:=decalageg+u*((simili)*0.4+0.2,0);
          else:
            for k=1 upto p_:
              trace Poids shifted(M1-lrcorner Poids-decalageg);
              decalageg:=decalageg+u*(0.6,0);
            endfor;
          fi;
        elseif string p_:
          nbimggauche:=nbimggauche+1;
          trace Imgg[nbimggauche] shifted(M1-decalageg-lrcorner Imgg[nbimggauche]);
          decalageg:=decalageg+(abs(llcorner Imgg[nbimggauche]-lrcorner Imgg[nbimggauche]),0)+u*(0.2,0);
        else:
          draw p_ shifted(M1-decalageg-lrcorner p_);
          decalageg:=decalageg+(abs(llcorner p_-lrcorner p_),0)+u*(0.2,0);
        fi;
      endfor;
      %
      nbimgdroit:=0;
      for p_=#2:
        if numeric p_:
          if Masse:
            trace PoidsM(p_) shifted(N1-llcorner PoidsM(p_)+decalaged);
            \ifemptyKV[Balance]{Vraisemblance}{simili:=1+0.5*(p_ div 5);}{simili:=\useKV[Balance]{Vraisemblance};}
            decalaged:=decalaged+u*((simili)*0.4+0.2,0);
          else:
            for k=1 upto p_:
              trace Poids shifted(N1-llcorner Poids+decalaged);
              decalaged:=decalaged+u*(0.6,0);
            endfor;
          fi;
        elseif string p_:
          nbimgdroit:=nbimgdroit+1;
          trace Imgd[nbimgdroit] shifted(N1+decalaged-llcorner Imgd[nbimgdroit]);
          decalaged:=decalaged+(abs(llcorner Imgd[nbimgdroit]-lrcorner Imgd[nbimgdroit]),0)+u*(0.2,0);
        else:
          draw p_ shifted(N1+decalaged-llcorner p_);
          decalaged:=decalaged+(abs(llcorner p_-lrcorner p_),0)+u*(0.2,0);
        fi;
      endfor;
      \ifPfCDeuxColonnes\relax
        Echelle=\mpdim{\linewidth};
        picture Retiens;
        Retiens=currentpicture;
        currentpicture:=nullpicture;
        draw Retiens scaled (Echelle/abs(lrcorner Retiens - llcorner Retiens));
      \fi
    \end{mplibcode}
}%